Cross-train all players in offensive and defensive
positions.
Substitute the entire line every play, so all players can
get ~4
plays of rest between each active play. (As currently
played, there is usually an offensive line and defensive
line of ~11 players each, and the line stays on the
field
until possession changes.)

At low levels, it may make sense to have the best
players play
most of the time. But at high levels, where the
differences
between players are smaller, it may be better to have
fresh
players in every play.

Training all players in all positions would also aid the
development of younger players, encourage team unity,
and
be more exciting to watch.

Do you watch much American football? Position specialty is
kind of a hallmark of the game. Vince Wilfork can't skin the
nickel off a dime with a 35-yard bullet pass, but neither
can Tom Brady run a forty with a Volkwagon Scirocco under
each arm. Shirley you aren't suggesting that these players,
widely considered to be among the finest in the NFL, could
find greater success by trading places?

Imagine playing a team sport where you spend much less than 50% of the time on field.

I mean cricket is bad enough in that respect, but at least it makes sense. I remember playing suburban division Rugby, where there were 5 players on the bench and a total of 5 substitutions allowed, all game (notwhithstanding the blood bin or send-off injuries, from which you couldn't return if substituted). You still specialised in position, but also had to be ready to fill a similar role if needed. More importantly, you ran your arse off for two 40 minute halves with little time for rest.

I think the proposal is quite sound, but football just isn't
the game for it. I believe pro athletes in other sports, such
as hockey, soccer, and basketball switch positions during
practice, and I'm certain I heard something about pro rugby
players being required to play every position.

Yeah, that's not really practical. One of the best features of Rugby (and by here I presume you mean rugby union, the original "Rugby", as opposed to rugby league, which is kind of devolved and lacks the sophistication) - is the mix of diversity and specialisation of position. A front rower should be able to catch, pass and kick like a fullback, but would never be expected to do so. I played a mix of hooker and tight-head prop for years, and my coach once said to me - "if I ever see you pass the ball again I'll stick my foot up your arse" - it's not that I passed badly, it's just passing isn't my job. Likewise, a fly half should be handy at the ruck and know how to maul, should be a good tackle - but their job is to not get involved. These specialisations obviously lend themselves to physical traits, in that front rowers are bulky and not too tall, fullbacks are tall and fast, and scrum halves are best described as rats, or perhaps mongooses, if you like that sort of thing.

What I'm saying is you'd never put a prop out to the wing, as they just couldn't physically do the job. Similarly, a fly half could not physically hold up their side of a scrum if put in as prop - they would literally break in half (and I mean that, it would be incredibly dangerous to attempt).

Have I mentioned before not to get me started on rugby?

As to the idea, I don't like it because I don't like being a spectator in a sport I'm supposed to be participating in. To my mind, the better option would be to just cut the team size down to a much smaller group, say half as many reserves as there are players, then instigate some rules controlling the frequency and overall number of substitutions made. Make the runners have to tackle. Make the catchers sometimes block, make the blocker sometimes run (and maybe even score). But overall, make everyone do more of everything, for the majority of the time. []

7 people line up and act at the same time. Each play most do something different. Subs just take too long to get with the program. If ends are running half way down the field, a bit of swapping makes sense.

TV gives you plenty of time to rest. Just the time the ref takes to reset chains or announce penalties is enough for most to recover.